Henry Ernest Dudeney/Modern Puzzles/Geometrical Problems/Dissection Puzzles

Henry Ernest Dudeney: Modern Puzzles: Geometrical Problems: Dissection Puzzles

$103$ - A New Cutting-out Puzzle

Cut the figure into four pieces that will fit together and form a square.

$104$ - The Square Table-Top

A man had three pieces of beautiful wood, measuring $12$ units, $15$ units and $16$ units square respectively.

He wanted to cut those into the fewest pieces possible that would fit together and form a small square table-tip $25$ units by $25$ units.

How was he to do it?

$105$ - The Squares of Veneer

A man has two squares of valuable veneer, each measuring $25$ units by $25$ units.

One piece he cut, in the manner shown in our illustration, in four parts that will form two squares,

one $20$ units by $20$ units, and the other $15$ units by $15$ units.

Simply join $C$ to $A$ and $D$ to $B$.

How is he to cut the other square into four pieces that will form again two other squares, with sides in exact units,

but not $20$ and $15$ as before?

$106$ - Dissecting the Moon

In how large a number of pieces can this crescent moon be cut with five straight cuts of the knife?

The pieces may not be piled or shifted after a cut.

$107$ - Dissecting the Letter E

Can you cut this letter $\text E$ into only five pieces so that they will fit together to form a perfect square?

All the measurements have been given so that there should be no doubt as to the correct proportions of the letter.

In this case you are not allowed to turn over any piece.

$108$ - Hexagon to Square

Can you cut a regular hexagon into $5$ pieces that will fit together to form a square?

$109$ - Squaring a Star

This six-pointed star can be cut into as few as five pieces that will fit together to form a perfect square.

To perform the feat in $7$ pieces is quite easy,

but to do it in $5$ is more difficult.

The dotted lines are there to show the true shape of the star, which is made of $12$ equilateral triangles.

$110$ - The Mutilated Cross

Here is a regular Greek cross from which has been cut a square piece exactly equal to one of the arms of the cross.

The puzzle is to cut what remains into four pieces that will fit together and form a square.

$111$ - The Victoria Cross

Cut the cross shown into seven pieces that will fit together and form a perfect square.

Of course, there must be no trickery or waste of material.

$112$ - Squaring the Swastika

Cut out the swastika and then cut it up into four pieces that will fit together and form a square.

$113$ - The Maltese Cross

Can you cut the star into four pieces and place them inside the frame so as to show a perfect Maltese cross?

$114$ - The Pirates' Flag

Here is a flag taken from a band of pirates on the high seas.

The twelve stripes represented the number of men in the band,

and when a new man was admitted or dropped out a new stripe was added or one removed, as the case might be.

Can you discover how the flag should be cut into as few pieces as possible so that they may be put together again and show only ten stripes?

No part of the material may be wasted, and the flag must retain its oblong shape.

$115$ - The Carpenter's Puzzle

A ship's carpenter had to stop a hole $12$ inches square,

and the only piece of wood that was available measured $9 \ \mathrm{in.}$ in breadth by $16 \ \mathrm{in.}$ length.

How did he cut it into only two pieces that would exactly fit the hole?

The answer is based on the "step principle", as shown in the diagram.

If you move the piece marked $B$ up one step to the left,

it will exactly fit on $A$ and form a perfect square measuring $12$ inches on every side.

This is very simple and obvious.

But nobody has ever attempted to explain the general law of the thing.

As a consequence, the notion seems to have got abroad that the method will apply to any rectangle where the proportion of length to breadth is within reasonable limits.

This is not so, and I have had to expose some bad blunders in the case of published puzzles that were supposed to be solved by an application of this step principle,

but were really impossible of solution.$^*$

Let the reader take different measurements, instead of $9 \ \mathrm{in.}$ by $16 \ \mathrm{in.}$,

and see if he [or she] can find other cases in which this trick will work in two pieces and form a perfect square.

$116$ - The Crescent and the Star

Here is a little puzzle on the Crescent and the Star.

Look at the illustration, and see if you can determine which is the larger, the Crescent or the Star.

If both were cut out of a sheet of solid gold, which would be more valuable?

As it is very difficult to guess by the eye,

I will state that the outer arc is a semicircle;

the radius of the inner arc is equal to the straight line $BC$;

the distance in a straight line from $A$ to $B$ is $12$ units,

and the point of the star, $D$, contains $3$ square units.